Mixed isotopic exponents

The exponents described by Saunders, sometimes called mixed isotopic exponents , are shown in Eq. (11.17). The exponent describes the relationship between the H/T isotope effect from substitution at site one (determined when protium is at site two), and the site-one D/T isotope effect (determined when deuterium is at site two). If the two sites are distinguished as giving primary and secondary isotope effects, the first exponent in Eq. (11.17) resembles the single-site Swain-Schaad exponent Eq. (11.9) for a primary isotope effect, and the second exponent in Eq. (11.17) resembles a single-site secondary Swain-Schaad exponent. However, the mixed isotopic exponents necessarily involve isotopic substitution at two sites and should not be confused with single-site Swain-Schaad exponents. 

The Swain-Schaad and RGM components of mixed isotopic exponents can be readily identified by first defining relevant isotope effects on isotope effects [37]. 

Figure 11.11. Example of competitive experiments used by Saunders et al. [89, 97] to measure isotope effects for mixed-isotope exponent determinations. The primary and secondary isotope effects were determined using the starting tritium activities of the bromide substrate, the product styrene, and the solvent ethanol, all at a kno A/n fractional...

The results of Cha et al. [90] illustrate these tendencies. Their isotope effect results give an unexceptional primary mixed exponent, r = 3.58 + 0.08, and a much larger secondary mixed exponent, = 10.2 + 2.0. These mixed exponents have been studied recently in several large-scale computational projects [14, 38, 47, 91]. Many other experimental studies [89, 92] involving mixed isotopic exponents are the subject of several reviews [93-96]. 

Effects of Mechanistic Complexity on Mixed Isotopic Exponents... 

Limits proposed by Kohen and Jensen [39] should not be considered with the single-site Swain-Schaad values discussed in this section. Kohen and Jensen [39] proposed that a value of 4.8 be treated as an upper limit in a non-tunneling system for a secondary isotope effect exponent defined as in Section 11.5 describing mixed-label experiments. As shown in Section 11.5, it useful to separate these mixed-label exponents into two factors one that arises from H/D/T substitutions, and one that arises from isotopic substitution that amounts to an isotope effect on an isotope effect. Also note that it is not straightforward to convert a mixed-label exponent based on D/T isotope effects into one based on H/D isotope effects as Eq. (11.9) shows for single-site exponents. 

Cha et al. provided the first experimental proof of hydrogen tunneling on an enzyme by reporting an elevated RS exponent for benzyl alcohol oxidation by yeast ADH (YADH) [10]. Isotope effects for benzyl alcohol oxidation were determined by the mixed-label tracer method, in which the primary and a-secondary positions of benzyl alcohol are either H or D, with stereochemically random, trace-level T incorporation. In this fashion, the observed ratios between the a-secondary (kH/feT)i H and (kD/feT)i°D KIEs are susceptible to both Swain-Schaad and RGM deviations and, thus, are sensitive probes for tuimeling (see Section 10.3.3.3). The observed a-secondary RS exponent, kn/feT = at 25 "C, greatly exceeded... 

Saunders Exponents Mixed Multiple Isotope Probes... 

---